In a triangle, one of the sides is 5cm, the other 7cm. What integers can be used to express the length of the third side?
| August 22, 2021 | education
Since we have the lengths of two sides of a triangle, we can use the triangle inequality – any side of a triangle is less than the sum of the other two sides and is greater than the difference between these sides.
Consider the upper figure, from which it can be seen that the length of C must be greater than the difference between the sides A and B, if C = B – A, then the points of the triangle lie on one straight line. Then C> (B – A), C> 2.
It can be seen from the lower figure that the length of C cannot be greater than the sum of the lengths of the other two sides. C <(A + B). C <12.
It turns out that one hundred C lies in the range 2 <C <12.
Integers in this range: 3, 4, 5, 6, 7, 8, 9, 10, 11.
Answer: 3, 4, 5, 6, 7, 8, 9, 10, 11.
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